Robust Numerical Methods for Singularly Perturbed Differential Equations [electronic resource] : Convection-Diffusion-Reaction and Flow Problems / by Hans-Görg Roos, Martin Stynes, Lutz Tobiska.

Ordinary Differential Equations -- The Analytical Behaviour of Solutions -- Numerical Methods for Second-Order Boundary Value Problems -- Parabolic Initial-Boundary Value Problems in One Space Dimension -- Analytical Behaviour of Solutions -- Finite Difference Methods -- Finite Element Methods -- Two Adaptive Methods -- Elliptic and Parabolic Problems in Several Space Dimensions -- Analytical Behaviour of Solutions -- Finite Difference Methods -- Finite Element Methods -- Time-Dependent Problems -- The Incompressible Navier-Stokes Equations -- Existence and Uniqueness Results -- Upwind Finite Element Method -- Higher-Order Methods of Streamline Diffusion Type -- Local Projection Stabilization for Equal-Order Interpolation -- Local Projection Method for Inf-Sup Stable Elements -- Mass Conservation for Coupled Flow-Transport Problems -- Adaptive Error Control.

This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations.